This project is designed to use mathematical and computational methods to develop models of individual dendrites, individual neurons, and neuron networks that are based on experimental data. Two projects have continued during FY2000. The first continues a theoretical analysis of why neuronal dendrites branch, based on morphological data obtained earlier in this laboratory. Using the symbolic manipulation package Mathematica, we have continued to investigate why the dendrites of most neurons branch extensively. The simplest hypothesis - that branching maximizes surface-to-volume ratios - can be falsified with a trivial counter-example. Our current view is that neurons that must receive large numbers and/or a great variety of synaptic contacts have to branch extensively in order to optimize packing density within the neuropil. The key element seems to be the volume fraction occupied by afferent axons, which can vary over a wide range depending on the organization of pre- and postsynaptic elements that must be accommodated. This hypothesis is completely consonant with our earlier hypothesis that dendrites branch in order to maximize the amount of synaptic current that can be delivered to the soma from synaptic sources that are distributed at relatively low density throughout the neuropil. In that idea, volume elements within 150 microns of the branches of simulated dendrites are each weighted by the calculated electrotonic connectivity to the soma of the nearest dendrite segment. This coupling-weighted external volume, when summed and divided by the internal dendrite volume, gives a coupled volume ratio (CVR) as the figure of merit to be optimized. Several morphological parameters are adjusted in a search algorithm to generate spatially idealized models whose CVRs are compared to actual motoneurons. Optimal values of the four parameters produced dendrites that resembled those in the target set of 60 dendrites from reconstructed cat motoneurons. We conclude that the ratio of external coupled volume to internal dendrite volume is a realistic figure of merit for neurons, and that motoneuron dendrites come reasonably close to optimal shapes for this figure of merit. We have also continued to improve work on visualizing the neuronal interactions that occur within the basic circuit that produces rhythmic respiration, based on experiments of Dr. Jeffrey Smith. The simulations permit visualization of the synchronization of individual neurons within the circuit, as well as the sequence of synaptic flows and membrane dynamics among the five cell types that shape the time course of respiration. We have begun a new project that concerns a computer modeling study of the effects of beta innervation of muscle spindles in mammals. Muscle spindles contain specialized muscle fibers that are innervated by two types (static and dynamic) of gamma motoneurons. In recent years it has become clear that many spindles also receive beta innervation from the motoneurons that also innervate the extrafusal skeletal muscle fibers that form the main bulk of muscles. Beta motoneurons that innervate slow twitch extrafusal muscle fibers produce static effects on spindle afferents, while those that innervate fast twitch fibers produce dynamic effects. Gamma motoneurons do not receive monosynaptic feedback from muscle spindle afferents but beta motoneurons do, with unknown functional consequences. Because the system is so complex, we are developing a multiple neuron simulation system that will enable us to explore the probable influence of positive excitatory feedback due to beta innervation among alpha and beta motoneurons. Finally, we are accumulating data on the morphology of motoneurons in the neonatal mouse spinal cord, labeled intracellularly with Biocytin. The cells are completely reconstructed and the data will be analyzed quantitatively using methods developed collaboratively by this laboratory and scientists at the Krasnow Institute of George Mason University. The data will form part of an extensive data base being developed as part of the Human Brain Project that is designed to permit scientists anywhere to access and analyze morphological data on many types of neurons.